といわず・であれ〜であれ・を問わず: the difference
Not only A or B but every-; A, B and every-; Not only A or B but all over; A, B both, whether A or B
食事中と言わず会話中と言わず携帯を手放さない娘が心配です。
My daughter never puts her phone down, at meals, in conversation, anywhere, and I'm worried.
Whether or, Or, No matter which, In either case
近代美術であれ伝統芸能であれ、芸術は芸術だ。
Whether it is modern art or traditional art, art is art.
Regardless of, Whether or not, No matter, With or without
Tested 2 times in past papers
どんな役かは問わず、とにかく舞台に立ちたい。
I don't care what role it is — I just want to be on stage.
How to tell them apart
「〜といわず〜といわず」: everywhere, day and night, with a flavour of being worn out or complaining.
「〜であれ〜であれ」: whichever it is, treat it the same; used for principles and rules, such as 'adults or children, all must follow the rules'.
「〜を問わず」: a single noun＋を問わず, neutrally 'regardless of', as in 「男女を問わず」 (regardless of gender).